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Research Papers

Chebyshev Wavelet Quasilinearization Scheme for Coupled Nonlinear Sine-Gordon Equations

[+] Author and Article Information
K. Harish Kumar

School of Basic Sciences,
Indian Institute of Technology Indore,
Indore 452017, India

V. Antony Vijesh

School of Basic Sciences,
Indian Institute of Technology Indore,
Indore 453552, India
e-mail: vijesh@iiti.ac.in

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 5, 2015; final manuscript received October 14, 2016; published online November 22, 2016. Assoc. Editor: Gabor Stepan.

J. Comput. Nonlinear Dynam 12(1), 011018 (Nov 22, 2016) (5 pages) Paper No: CND-15-1058; doi: 10.1115/1.4035056 History: Received March 05, 2015; Revised October 14, 2016

Radial basis function (RBF) has been found useful for solving coupled sine-Gordon equation with initial and boundary conditions. Though this approach produces moderate accuracy in a larger domain, it requires more grid points. In the present study, we develop an alternative numerical scheme for solving one-dimensional coupled sine-Gordon equation to improve accuracy and to reduce grid points. To achieve these objectives, we make use of a wavelet scheme and solve coupled sine-Gordon equation. Based on the numerical results from the wavelet-based scheme, we conclude that our proposed method is more efficient than the radial basic function method in terms of accuracy.

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Topics: Wavelets
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Figures

Grahic Jump Location
Fig. 1

Numerical and exact solutions of u(x, t) and w(x, t) at t = 2 for Example 4.1

Grahic Jump Location
Fig. 2

Numerical and exact solutions of u(x, t) and w(x, t) at t = 0.3 for Example 4.2

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